531
OPTION TrAdINg STrATegIeS
It should be obvious that such risk-free profit opportunities will be limited in terms of 
both duration and magnitude. generally speaking, conversion and reverse conversion arbitrage 
will normally only be feasible for professional arbitrageurs who enjoy much lower transac-
tion costs (commissions plus execution costs) than the general public. The activity of these 
arbitrageurs will tend to keep synthetic futures position prices about in line with actual futures 
prices.
Strategy 16: Synthetic Short Futures (Long put + Short Call)
example. Buy an August $1,300 gold futures put at a premium of $108.70/oz ($10,870) and simul-
taneously sell an August $1,300 gold futures call at a premium of $9.10/oz ($910). (See Table 35.16 
and Figure 35.16.)
Comment. As follows directly from the discussion of the previous strategy, a synthetic short futures 
position can be created by combining a long put and a short call with the same expiration date and the same 
strike price. In this example, the synthetic futures position based upon the $1,300 strike price options 
is $0.40 higher priced than the underlying futures contract. (Synthetic futures position = $1,300 
+ $9.10 − $108.70 = $1,200.40.) However, for reasons similar to those discussed in the previous 
strategy, much of the advantage of an implied synthetic futures position price versus the actual futures 
price typically disappears once transaction costs and interest income effects are incorporated into the 
evaluation. An arbitrage employing the synthetic short futures position is called a conversion and was 
detailed in the previous strategy.
tabLe 35.16 profit/Loss Calculations: Synthetic Short Futures (Long put + Short Call)
(1) (2) (3) (4) (5) (6) (7) (8)
Futures 
price at 
expiration 
($/oz)
premium of 
august $1,300 
Call at Initiation 
($/oz)
Dollar 
amount of 
premium 
received
premium of 
august $1,300 
put at Initiation 
($/oz)
Dollar 
amount of 
premium 
paid
Value of 
Call at 
expiration
Value of 
put at 
expiration
profit/Loss on 
position  
[(3) − (5) + (7) − (6)]
1,000 9.1 $910 108.7 $10,870 $0 $30,000 $20,040
1,050 9.1 $910 108.7 $10,870 $0 $25,000 $15,040
1,100 9.1 $910 108.7 $10,870 $0 $20,000 $10,040
1,150 9.1 $910 108.7 $10,870 $0 $15,000 $5,040
1,200 9.1 $910 108.7 $10,870 $0 $10,000 $40
1,250 9.1 $910 108.7 $10,870 $0 $5,000 –$4,960
1,300 9.1 $910 108.7 $10,870 $0 $0 –$9,960
1,350 9.1 $910 108.7 $10,870 $5,000 $0 –$14,960
1,400 9.1 $910 108.7 $10,870 $10,000 $0 –$19,960